Mathematical analyses and models are powerful tools for understanding physiology and effectively using[unreadable] research resources. Mathematical analyses enable extraction of additional information from data sets.[unreadable] Mathematical modeling forces explicit definition of the variables involved, their response to stimuli and their[unreadable] interactions, and frequently clarifies areas of fruitful future experimentation and intervention. For this[unreadable] proposal, the Analytic Core helped develop the experimental protocols. Each of the experimental Projects[unreadable] will do primary and secondary analyses of their data sets. The Analytic Core will extend their work by[unreadable] providing more detailed mathematical analyses and modeling by using data from multiple projects, as well as[unreadable] by developing and applying more sophisticated mathematical techniques and modeling tools. The[unreadable] development of new mathematical analyses and models of biological systems is a complicated process,[unreadable] ideally involving understanding of the biology and mathematics and interactions of the experimenters and[unreadable] mathematicians. An Analytic Core within a Program Project Grant is an ideal situation for such work.[unreadable] The Specific Aims are to: (1) To develop and quantify the relative merits of different measures of short-term[unreadable] (within a bedrest episode) and long term (across bedrest episodes) sleep drive (or "pressure") within a[unreadable] bedrest episode and to quantify how these measures of sleep drive are affected by circadian phase, time[unreadable] within a bedrest episode, chronic sleep restriction (CSR) and age; (2) To apply these analyses to data on[unreadable] human and rat sleep and wake bouts and to quantify the similarities and differences between human and[unreadable] rodent models; (3) To develop and quantify the relative merits of different measures of short-term and[unreadable] longer-term sleep drive on subjective alertness and objective neurobehavioral performance within a wake[unreadable] episode and to quantify how these measures of wake-time alertness and performance vary with circadian[unreadable] phase, time within a wake episode, CSR, and age.; (4) To apply these analyses and analyses from Core C[unreadable] (Polysomnographic Core) to quantify the inter-relationships of sleep drive and metabolic changes during[unreadable] CSR; and (5) To continue development of a mathematical model of the human circadian pacemaker and its[unreadable] effects on sleep, subjective alertness and objective neurobehavioral performance.[unreadable] The Analytic Core will develop and test mathematical analyses and modeling applicable to many projects.